Besides WPT, the UAV uses most energy for its movement. Thus, to extend the operating time, the UAV is considered to hover at a fixed position at the central of the cluster. For this scenario, we formulate the MDP [1]} by a 4-tuple \(< \mathcal {S}, \mathcal {A}, \mathcal {P}, \mathcal {R} >\)  where \(\mathcal {S}, \mathcal {A}\)  are is the agent's state space and action space, respectively; \(\mathcal {P}_{ss^{\prime }}(a)\)  is the state transition probability with \(s = s^t, s^{\prime } =s^{t+1} \in \mathcal {S}\) , \(a \in \mathcal {A}\) ; \(\mathcal {R}\)  is the reward function. Then, we formulate a game to solve the problem in Equ. (REF ).
